The rational ground given by Leibniz to the monads in his works is quintuple:
The Monadology is written in ninety short logical paragraphs, each generally following on from the previous. Its name is due to the fact that Leibniz, imitating Marsilio Ficino, Giordano Bruno and Anne Conway, wanted to keep together the meanings of “monas” (in Greek, “unity”) and “logos (λογος)” (“treatise” or “science”, literally "word" or "reason"). Therefore, the Monadology came to be the monad’s treatise or the science of the unity.
The text is reasoned in a dialectical way, facing questions and problems that help the reader to advance in his learning. Thus, for instance, it can be accepted that composed bodies are something derived, extended, phenomenical or repeated according to simple substances (which will be later expressed by Kant in his dichotomy phenomena-noumena). Is the soul a monad? If the answer is affirmative, then the soul is a simple substance. If it is an aggregate of matter, then it cannot be a monad.
Leibniz characterizes monads as metaphysical points, animate points or metaphysical atoms. In contrast to those physical atoms postulated by classic atomism they are not extended and thus are no bodies. But, as Leibniz explains in his letters to Burchard de Volder and Bartholomew des Bosses, this does not imply, that monads are immaterial. They rather consist of two principles inseparable from each other and constituting together a complete substance or monad: the innermost center of a monad, i.e. the mathematical point, where the entelechy, soul or spirit is located, is the inner form of a monad. This form has no existence in itself, but is incarnated in a physical point or an infinitesimally small sphere, which is the "vehicle of the soul". This hull consists of a special matter, called primary matter (materia prima, matière primitive).
The problem that monads are supposed to have some kind of matter on the one hand, but to have any parts and no extension on the other hand, is to be explained by the dynamic nature of primary matter. Leibniz conceives primary matter in contrast to the second matter (materia secunda), i.e. extended and purely phenomenal bodies. Primary matter is a very fine, fluid and elastic matter, which he identifies in his early "Hypothesis physica nova" (1671) with the aether, spiritus or matter of light, flowing anywhere through every body. Strictly taken, this primary matter or matter of light does not consist in "extension, but in the desire to extension". Thus, "the nature of light strives to extend itself".
The animate centre of a monad can never exist without the encasing coating fluid of light, because firstly monads without this passive principle could never perceive any impressions from the exterior world, and because secondly they would have no limitation of power. "It follows that God can never strip any created substance bare of its primary matter, even though by his absolute power he can take off her secondary matter; otherwise he would make it become pure activity, which can only be himself." Only God is free from any matter, he is the creating first monad, out of which all created monads derive by continuous "effulgurations". The punch-line of the monad or metaphysical point is its dynamical unity of the mathematical centre and the encasing physical point: The fluid ethereal sphere of the monad is extended, has parts and can be destroyed, but in every deformation or division of the sphere the mathematical point in which the soul is incarnated shall outlive within the smallest remaining fluid. Indestructible therefore is not the whole sphere consisting in matter of light, but only the dynamic point within the monad.
Leibniz understands the monad as the intellectual answer to the mind-body-problem, exposed in its most radical form by René Descartes (1596-1650). Because Leibniz conceives the soul (not the monad) as an immaterial centre, he denies any direct interaction or physical influence (influxus physicus) between body and soul. He allocates the causal connection between both within the monad, because its fluid ethereal matter is the substantial bond (vinculum substantiale) between body and mind. The circulation of the aether or matter of light through the visible worldly bodies is the pre-established divine ‘artifice’, which constitutes the exact correspondence and harmony between the perceptions of the soul and the movements of the bodies. For this reason the pre-established harmony does not only govern the relation between body and soul, but also between monads.
According to Leibniz’s famous slogan, monads have "no windows" or portals, through which something could enter from the outside or could escape from the inside. Since the centre of the monad in which the soul is incarnated is always encased by its own primary matter. Despite that, the monad represents in a spontaneous act the surrounding world with an individual perspective, constituted by its punctual structure of centre, radius and circumference.
Hubertus Busche: Monade und Licht. Die geheime Verbindung von Physik und Metaphysik bei Leibniz, in: C. Bohlmann, T. Fink, P. Weiss (Ed.): Lichtgefüge des 17. Jahrhunderts. Rembrandt und Vermeer, Leibniz und Spinoza, München 2008, 125-162.
When it was written, the Monadology tried to put an end from a monist point of view to the main question of what is reality, and particularly to the problem of communication of substances, both studied by Descartes called mind-body dualism. Thus, Leibniz offered a new solution to mind and matter interaction by means of a pre-established harmony expressed as Best of all possible worlds form of optimism); in other words, he drew the relationship between “the kingdom of final causes”, or teleological ones, and “the kingdom of efficient causes”, or mechanical ones, which was not causal, but synchronous. So, monads and matter are only apparently linked, and there is not even any communication between different monads, as far as they act according to their degree of distinction only, as they were influenced by bodies, and vice versa.
Leibniz fought against the Cartesian dualist system in his Monadology and tried to surpass it through a metaphysical system considered at the same time monist (since only the unextended is substantial) and pluralist (as far as substances are disseminated in the world in an infinite number). For that reason the monad is an irreducible force, which makes it possible for the bodies to have the characteristics of inertia and impenetrability, and which contains in itself the source of all its actions. Monads are the first elements of every composed thing.
Monads are manifest, since they are everywhere, and there is no extension without monads. They are, then, the plenum, that is to say, the condition of an infinitely dense universe, but nevertheless they are unextended. However, this doesn’t mean that they lack of any function (as far as they project and reflect force), matter (since they come with it) or that they are extended (considering that they don’t interact with anything in the world).
Extended matter would be the impenetrable quality of the unextended—the monad, without any doors or windows—as passively transmitted according to movements which, together with perception and apperception, compose action. In spite of that, monad cannot remain placed in matter, which follows the monad itself, previously to the generation of matter in time. So, extension and monads coexist acausally by the means of a timeless creation, although they are reciprocally bound according to the appearances.
In brief, Leibniz states that matter is extended, but not only extended. It is, in addition, formed by unextended monads. Then, is matter both extended and unextended? No, accepting that, as far as monad constitutes matter, matter is nothing in itself, as an isolated being.
This theory leads to:
1. Idealism, since it denies things in themselves (besides monads) and multiplies them in different points of view. Monads are “perpetual living mirrors of the universe”.
2. Metaphysical optimism, through the principle of sufficient reason, developed as follows:
a) Everything exists according to a reason (by the axiom "Nothing arises from nothing");
b) Everything which exists has a sufficient reason to exist;
c) Everything which exists is better than anything non-existent (by the first point: since it is more rational, it also has more reality), and, consequently, it is the best possible being in the best of all possible worlds (by the axiom: "That which contains more reality is better than that which contains less reality").
The “best of possible worlds”, then, is that “containing the greatest variety of phenomena from the smallest amount of principles”.